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prob_06_04_01

# prob_06_04_01 - Problem 6.4-1 Given Consider two adjacent...

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Problem 6.4-1 Given: Consider two adjacent plane quadratic elements, as shown. Show that the shape functions provide interelement continuity of the field quanity along the boundary. Solution: Along the right edge of the left element: ξ 1 := N 2 1 4 1 ξ + ( ) 1 η ( ) 1 4 1 ξ 2 ( ) 1 η ( ) 1 4 1 ξ + ( ) 1 η 2 ( ) = N 2 η 2 2 η 2 = N 3 1 4 1 ξ + ( ) 1 η + ( ) 1 4 1 ξ + ( ) 1 η 2 ( ) 1 4 1 ξ 2 ( ) 1 η + ( ) = N 3 η 2 2 η 2 + = N 6 1 2 1 ξ + ( ) 1 η 2 ( ) = N 6 1 η 2 = let ϕ A ϕ 2 = ϕ B ϕ 3 = ϕ C ϕ 6 = ϕ N 2 ϕ A N 3 ϕ B + N 6 ϕ C + = η 2 η 2 ϕ A η η 2 + 2 ϕ B + 1 η 2 ( ) ϕ C + = Along the left edge of the right element: ξ 1 := N 1 1 4 1 ξ ( ) 1 η ( ) 1 4 1 ξ 2 ( ) 1 η ( ) 1 4 1 ξ ( ) 1 η 2 ( ) = N 1 η 2 2 η 2 = N 4 1 4 1 ξ ( ) 1 η + ( ) 1 4 1 ξ 2 ( ) 1 η + ( ) 1
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